# The Influence of Climate Variability Effects on Groundwater Time Series in the Lower Central Plains of Thailand

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}and has 8 layers of groundwater, with Bangkok clay on the top. All other boundary values were set to be steady. The calibration was done using the data of 325 observed wells. The normalized RMS value was 9.705%. The results were verified by the data using ARIMAX over the same time periods. To conclude, the simulated results of the monthly groundwater level in 2012 of the wells have a confidence interval of around 95%, which is near the result from the ARIMAX model. The advantages of the ARIMAX model include high accuracy, no requirement for a large amount of data and inexpensive implementation. It is one of the effective tools for the groundwater prediction.

## 1. Introduction

## 2. Linkages between Climate Variability and Water Resources

## 3. Study Area

^{2}and has the biggest groundwater basin in Thailand, at 269.312 billion m

^{3}. The area can be divided into 2 major parts. The lower plains part covers the area from the plain in Manorom city in Chainat province to the estuary area of the Chao Phraya River, which contains the water from the ground level to about 600 m deep. The other part is the borders of the Chao Phraya basin on both the east and west side, which is a mountainous area and has less water. The west side of the Chao Phraya basin edge covers the area from Uthai Thani province and the west side of Suphanburi province to Nakorn Pathom province. The east side of the Chao Phraya basin edge covers the area from Lopburi province, Saraburi province, Nakorn Nayok province, Prachinburi province and Cha Choeng Sao province.

## 4. Methodology

#### 4.1. Available Data

#### 4.1.1. Climatic Indices Data

#### 4.1.2. Groundwater Data

#### 4.2. Theory

^{2}) and covariance (γ). Therefore, the characteristics of the data need to be inspected with the unit root test, which can be done by using the Augmented Dicky-Fuller Test (ADF) [52] in 3 forms, as shown in Equations (1)–(3).

_{t}will have a unit root from comparing the calculated t-statistic value and the value from the Dickey-Fuller tables, or the MacKinnon critical values.

#### 4.2.1. ARIMA Model

_{t}value; it was assigned from the values of y

_{t−1},...,y

_{t−p}or the previous observed value (p) by using the process of system AR(p), which is the process of the Autoregressive system at p order, which can be written as shown in Equation (4).

_{t}is the groundwater level at time t; μ is the constant value; φ

_{i}is the I ordered parameter; and ε

_{t}is the error at time t.

_{t}value, which is assigned from the error at ε

_{t−1},…,ε

_{t−q}or the previous error by using the process or system MA(q), which is the Moving Average at the q order, which can be written as in Equation (5).

_{t}is the groundwater level at time t; p is the order of Autoregressive; d is the number of times that differences were found in the constant characteristic time series data; q is the order of Moving Average; ∆

_{d}is the sign of finding the difference at d ordered (d-th difference operator); δ is the constant value; φ

_{1}, φ

_{p}is the parameter of Autoregressive; θ

_{1}, θ

_{q}is the parameter of Moving Average; ε

_{t}is the error at the time t, which has been assigned to be white noise; and t is the time index.

#### 4.2.2. ARIMAX Model

_{t}is the climate/oceanography index, where θ(L) is the degree of polynomial of the Exogenous variable that affects the Endogenous variable.

_{0}: X does not influence Y) which can be said that to conclude that X influences Y, the null hypothesis needs to be rejected and when the variable passes the leading index testing, that variable could then be used to analyze the ARIMAX model.

## 5. Conceptual Groundwater Model

^{2}, the model has a total of 945,000 grids, which are divided into 9 layers, comprising 8 layers of groundwater and the average 20-m thick Bangkok clay as the top layer.

#### 5.1. Boundary

#### 5.2. Parameters

#### 5.3. Simulation Scenarios

## 6. Results and Discussion

#### 6.1. Unit Root Test

_{0}: θ = 0), which means that this data set had unit root. Then, the time series data was adjusted to be stationary by transforming the time series data with the 1st difference. When the adjusted data was retested with the ADF, the results showed that the ADF test statistic values were all higher than the critical value at the 0.01 and 0.05 significance level. This means that the 1st differential data were suitable for developing the ARIMA and ARIMAX model for forecasting the groundwater level in the study area, as shown in Table 4.

#### 6.2. Identification

_{t}. On the other hand, the coefficient of AR(4) is 0.169. The t-statistic value is 3.079, which is far from 0, with the significance level at 0.05. This means that the change of AR(4) is in the same direction with ∆y

_{t}. The coefficient of MA(1) is 0.891 and the t-statistic value is 18.618, which is different from 0, with the significance level at 0.05. This means that the change of MA(1) is in the same direction as ∆y

_{t}.

#### 6.3. Parameter Estimation

#### 6.4. Diagnostics

_{t}) show that the correlogram of residuals of autocorrelation (ACF) show no sign of exponential regression. At the same time, the calculated Box and Ljung (Q-statistic) value is lower that the critical value of Chi-square at the 0.10 significance level (prob. < 0.10), which means that ε

_{t}is white noise or has normal distribution. The mean is equal to 0 and variances σ

_{2}, so it could be said that ε

_{t}has no autocorrelation and no heteroscedasticity. Table 7 shows the analytic results, showing that all the time series samples passed the diagnostic checking and were suitable for use in forecasting.

#### 6.5. ARIMAX

_{0}: The test index was not the cause of groundwater level” and accepted the hypothesis “H

_{0}: The groundwater level was not the cause of the text index”. The test results of each station for the ARIMAX model are shown in Table 9.

#### 6.6. MODFLOW Simulation in Steady State

#### 6.7. Comparison of ARIMAX Groundwater Level and MODFLOW Groundwater Level

## 7. Conclusions

_{t}) by the Box and Ljung process (Q-statistic); in this step, it was found that every selected form was appropriate. The Granger Causality Test of the leading parameters and climate indices was applied to see which index could be used in the ARIMAX model and could forecast the groundwater level for 2012. The results showed that the groundwater level was related to the climate index and could give an effective forecast result at the approximate average RMSE of 0.6. The MODFLOW model then was developed for the study area, with 8 groundwater layers and topped with Bangkok clay. Other boundaries were set to be steady. The verification was done according to the procedure giving the monthly groundwater level result in 2012 at the 95% confidence interval, close to those from the ARIMAX modelling.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 11.**Comparison of groundwater level in the Ex-ante forecast by the ARIMAX(0,1,4) model for the CT17/2 station.

**Figure 13.**Equipotential line and flow direction results in the steady state: (

**a**) Layer 1; (

**b**) Layer 2.

**Figure 15.**Comparison of forecast groundwater levels between ARIMAX and MODFLOW, examples for (

**a**) CT17/2 and (

**b**) CT22/3 stations.

Top to the Deepest | Aquifers | h_{f} (m) |
---|---|---|

1 | Bangkok (BK) | 1.00 |

2 | Phra Pradaeng (PD) | 2.25 |

3 | Nakorn Luang (NL) | 4.0 |

4 | Nonthaburi (NB) | 6.25 |

5 | Sam Khok (SK) | 7.5 |

6 | Phaya Thai (PT) | 8.75 |

7 | Thonburi (TB) | 11.25 |

8 | Pak Nam (PN) | 13.75 |

Zone | Kx (m/s) | Ky (m/s) | Kz (m/s) |
---|---|---|---|

1 | 3.50 × 10^{−9} | 3.50 × 10^{−9} | 3.50 × 10^{−10} |

2 | 1.50 × 10^{−2} | 1.50 × 10^{−2} | 1.50 × 10^{−3} |

3 | 9.50 × 10^{−7} | 9.50 × 10^{−7} | 9.50 × 10^{−8} |

4 | 9.00 × 10^{−5} | 9.00 × 10^{−5} | 9.00 × 10^{−6} |

5 | 3.50 × 10^{−6} | 3.50 × 10^{−6} | 3.50 × 10^{−7} |

6 | 3.00 × 10^{−7} | 3.00 × 10^{−7} | 3.00 × 10^{−8} |

7 | 8.50 × 10^{−8} | 8.50 × 10^{−8} | 8.50 × 10^{−9} |

8 | 1.50 × 10^{−6} | 1.50 × 10^{−6} | 1.50 × 10^{−7} |

9 | 3.00 × 10^{−9} | 3.00 × 10^{−9} | 3.00 × 10^{−10} |

10 | 8.00 × 10^{−5} | 8.00 × 10^{−5} | 8.00 × 10^{−6} |

11 | 2.00 × 10^{−10} | 2.00 × 10^{−10} | 2.00 × 10^{−11} |

12 | 1.00 × 10^{−6} | 1.00 × 10^{−6} | 1.00 × 10^{−7} |

13 | 8.00 × 10^{−4} | 8.00 × 10^{−4} | 8.00 × 10^{−5} |

14 | 8.00 × 10^{−8} | 8.00 × 10^{−8} | 8.00 × 10^{−9} |

15 | 6.30 × 10^{−4} | 6.30 × 10^{−4} | 6.30 × 10^{−5} |

16 | 5.70 × 10^{−6} | 5.70 × 10^{−6} | 5.70 × 10^{−7} |

17 | 1.00 × 10^{−9} | 1.00 × 10^{−9} | 1.00 × 10^{−10} |

River | River Stage (m. msl.) | Riverbed Bottom (m. msl.) |
---|---|---|

Mae Klong River | 2.274–(−5.785) | 0.311–(−6.625) |

Tha Chin River | (−0.289)–(−2.694) | (−2.828)–(−4.328) |

Chao Phraya River | (−3.252)–(−2.928) | (−9.673)–(−12.075) |

Pa Sak River | 11.486–(−2.417) | 7.606–(−12.698) |

Station | Level | First Difference | ||||
---|---|---|---|---|---|---|

ADF | MacKinnon Critical | ADF | MacKinnon Critical | |||

1% | 5% | 1% | 5% | |||

CT4 | −0.603 | −3.983 | −3.422 | −20.590 | −3.983 | −3.422 |

CT5/2 | 1.713 | −3.983 | −3.422 | −14.080 | −3.983 | −3.422 |

CT7/1 | 0.013 | −3.983 | −3.422 | −14.156 | −3.983 | −3.422 |

CT17/2 | −1.301 | −3.983 | −3.422 | −15.747 | −3.983 | −3.422 |

CT22/3 | −0.101 | −3.983 | −3.422 | −11.451 | −3.983 | −3.422 |

CT23 | −0.761 | −3.983 | −3.422 | −22.690 | −3.983 | −3.422 |

CT26/1 | 0.230 | −3.983 | −3.422 | −19.002 | −3.983 | −3.422 |

CT27 | 0.916 | −3.983 | −3.422 | −19.491 | −3.983 | −3.422 |

CT30/1 | −0.639 | −3.983 | −3.422 | −13.330 | −3.983 | −3.422 |

CT31/2 | −2.816 | −3.983 | −3.422 | −6.091 | −3.984 | −3.422 |

CT33/2 | 0.143 | −3.983 | −3.422 | −22.445 | −3.983 | −3.422 |

CT35/2 | 1.225 | −3.983 | −3.422 | −16.313 | −3.983 | −3.422 |

CT45 | −0.342 | −3.983 | −3.422 | −21.881 | −3.983 | −3.422 |

CT48/2 | −1.663 | −3.983 | −3.422 | −21.548 | −3.983 | −3.422 |

Observation Wells | Seasonal | Model | BIC | Proper Model |
---|---|---|---|---|

CT4 | None | ARIMA(0,1,2) | −2.358 | ARIMA(0,1,2) |

CT5/2 | None | ARIMA(1,1,10) | −0.974 | ARIMA(1,1,10) |

None | ARIMA(0,2,4) | −0.997 | ||

CT7/1 | None | ARIMA(0,1,3) | −2.09 | ARIMA(0,1,4) |

None | ARIMA(0,1,4) | −2.086 | ||

CT17/2 | None | ARIMA(1,1,0) | −0.485 | ARIMA(0,1,4) |

None | ARIMA(0,1,4) | −0.468 | ||

CT22/3 | None | ARIMA(2,1,0) | −1.291 | ARIMA(2,1,0) |

None | ARIMA(1,1,1) | −1.303 | ||

CT23 | None | ARIMA(0,1,1) | −1.732 | ARIMA(0,1,1) |

CT26/1 | None | ARIMA(4,1,0) | −1.812 | ARIMA(4,1,0) |

None | ARIMA(1,1,1) | −1.89 | ||

CT27 | None | ARIMA(4,1,0) | −2.845 | ARIMA(4,1,0) |

None | ARIMA(1,1,1) | −2.899 | ||

CT30/1 | None | ARIMA(2,1,0) | −2.334 | ARIMA(2,1,0) |

None | ARIMA(0,1,2) | −2.337 | ||

CT31/2 | None | ARIMA(0,1,0) | −1.744 | ARIMA(0,1,0) |

CT33/2 | None | ARIMA(1,1,2) | −0.38 | ARIMA(1,1,2) |

None | ARIMA(2,1,1) | −0.381 | ||

CT35/2 | None | ARIMA(13,1,0) | −2.893 | ARIMA(13,1,0) |

None | ARIMA(0,1,13) | −2.9 | ||

CT45 | None | ARIMA(1,1,6) | −0.783 | ARIMA(1,1,6) |

None | ARIMA(1,2,2) | −0.847 | ||

CT48/2 | None | ARIMA(1,2,4) | −0.57 | ARIMA(4,1,1) |

None | ARIMA(4,1,1) | −0.577 |

Variable | Coefficient | Std. Error | t-Statistic | Prob. |
---|---|---|---|---|

Constant | −0.033 | 0.102 | −0.326 | 0.745 |

AR(4) | 0.169 | 0.055 | 3.079 | 0.002 |

MA(1) | 0.891 | 0.048 | 18.618 | 0.000 |

R-squared | 0.996 | Ljung-Box Q | ||

BIC | −0.570 | 18.634 | 0.135 |

Station | Model | Ljung-Box Q | Prob. |
---|---|---|---|

CT4 | ARIMA(0,1,2) | 12.369 | 0.718 |

CT5/2 | ARIMA(1,1,10) | 25.831 | 0.072 |

CT7/1 | ARIMA(0,1,4) | 29.503 | 0.109 |

CT17/2 | ARIMA(0,1,4) | 10.213 | 0.746 |

CT22/3 | ARIMA(2,1,0) | 22.271 | 0.135 |

CT23 | ARIMA(0,1,1) | 7.976 | 0.967 |

CT26/1 | ARIMA(4,1,0) | 26.044 | 0.126 |

CT27 | ARIMA(4,1,0) | 25.131 | 0.083 |

CT30/1 | ARIMA(2,1,0) | 12.025 | 0.742 |

CT31/2 | ARIMA(0,1,0) | 11.225 | 0.885 |

CT33/2 | ARIMA(1,1,2) | 14.047 | 0.522 |

CT35/2 | ARIMA(13,1,0) | 10.337 | 0.066 |

CT45 | ARIMA(1,1,6) | 12.591 | 0.321 |

CT48/2 | ARIMA(1,2,4) | 17.876 | 0.162 |

Index | Lag (Months) | p-Value of H_{0} : | p-Value of H_{0} : | ||
---|---|---|---|---|---|

Index | GW Level | ||||

Has No Granger Causality | Has No Granger Causality | ||||

GW Level | Index | ||||

DMI | - | - | - | - | - |

IMI | 1 | 0.0319 | Reject | 0.6674 | Accept |

MEI | 3 | 0.0342 | Reject | 0.9747 | Accept |

NINO4 | - | - | - | - | - |

SOI | 3 | 0.0145 | Reject | 0.8931 | Accept |

WNPMI | 1 | 0.0318 | Reject | 0.9254 | Accept |

Station | Model | BIC | Ljung-Box Q | ||
---|---|---|---|---|---|

CT4 | ∆y | constant | MA(2) DMI(-3) IMI(-2) NINO4(-3) | −2.307 | 9.172 |

CT5/2 | ∆y | constant | AR(1) MA(10) DMI(-3) IMI(-3) MEI(-3) WNPMI(-2) | −0.900 | 7.407 |

CT7/1 | ∆y | constant | MA(4) DMI(-1) SOI(-1) | −2.053 | 18.051 |

CT17/2 | ∆y | constant | MA(4) MEI(-1) NINO4(-2) SOI(-1) | −0.437 | 7.840 |

CT22/3 | ∆y | constant | AR(2) DMI(-1) IMI(-1) MEI(-1) | −1.241 | 20.781 |

CT23 | ∆y | constant | MA(1) IMI(-2) SOI(-10) WNPMI(-2) | −1.672 | 6.874 |

CT26/1 | ∆y | constant | AR(4) DMI(-3) IMI(-1) | −1.788 | 21.647 |

CT27 | ∆y | constant | AR(4) IMI(-3) MEI(-3) SOI(-2) WNPMI(-2) | −2.780 | 18.694 |

CT30/1 | ∆y | constant | AR(2) IMI(-1) MEI(-3) SOI(-3) WNPMI(-1) | −2.290 | 14.131 |

CT31/2 | ∆y | constant | NINO4(-2) SOI(-2) | −1.720 | 11.206 |

CT33/2 | ∆y | constant | AR(1) MA(2) IMI(-1) WNPMI(-3) | −0.376 | 15.899 |

CT35/2 | ∆y | constant | AR(13) IMI(-1) SOI(-1) WNPMI(-4) | −2.893 | 7.994 |

CT45 | ∆y | constant | AR(1) MA(6) DMI(-7) IMI(-4) WNPMI(-5) | −0.732 | 13.977 |

CT48/2 | ∆y | constant | AR(4) MA(1) IMI(-5) MEI(-1) NINO4(-4) SOI(-1) | −0.513 | 16.629 |

Station | Model | (1) | (2) | (3) = (1)/(2) |
---|---|---|---|---|

RMSE | RMSE | RRMSE | ||

(ARIMA) | (ARIMAX) | – | ||

CT4 | ARIMA(0,1,2) | 0.357 | 0.130 | 2.746 |

CT5/2 | ARIMA(1,1,10) | 0.223 | 0.159 | 1.404 |

CT7/1 | ARIMA(0,1,4) | 0.646 | 0.439 | 1.472 |

CT17/2 | ARIMA(0,1,4) | 0.717 | 0.645 | 1.111 |

CT22/3 | ARIMA(2,1,0) | 0.167 | 0.152 | 1.097 |

CT23 | ARIMA(0,1,1) | 0.398 | 0.118 | 3.386 |

CT26/1 | ARIMA(4,1,0) | 0.077 | 0.075 | 1.023 |

CT27 | ARIMA(1,1,1) | 0.304 | 0.128 | 2.373 |

CT30/1 | ARIMA(2,1,0) | 0.481 | 0.108 | 4.469 |

CT31/2 | ARIMA(0,1,0) | 0.809 | 0.450 | 1.800 |

CT33/2 | ARIMA(2,1,1) | 1.239 | 0.330 | 3.754 |

CT35/2 | ARIMA(13,1,0) | 0.229 | 0.027 | 8.463 |

CT45 | ARIMA(1,1,6) | 0.420 | 0.098 | 4.307 |

CT48/2 | ARIMA(4,1,1) | 0.514 | 0.123 | 4.178 |

Layer | Kx [m/s] | Ky [m/s] | Kz [m/s] |
---|---|---|---|

1 | 5.5 × 10 ^{−9} | 5.5 × 10 ^{−9} | 5.5 × 10 ^{−10} |

2 | 0.00968 | 0.00968 | 0.000968 |

3 | 0.0099 | 0.0099 | 0.0099 |

4 | 0.0001 | 0.0001 | 1 × 10 ^{−6} |

5 | 2.26 × 10 ^{−6} | 2.26 × 10 ^{−6} | 2.26 × 10 ^{−7} |

6 | 2.23 × 10 ^{−7} | 2.23 × 10 ^{−7} | 2.23 × 10 ^{−8} |

7 | 1.07 × 10 ^{−7} | 1.07 × 10 ^{−7} | 1.07 × 10 ^{−9} |

8 | 2.76 × 10 ^{−6} | 2.76 × 10 ^{−6} | 2.76 × 10 ^{−7} |

9 | 4.38 × 10 ^{−10} | 4.38 × 10 ^{−10} | 4.38 × 10 ^{−11} |

10 | 4 × 10 ^{−9} | 4 × 10 ^{−9} | 4 × 10 ^{−10} |

11 | 4.85 × 10 ^{−5} | 4.85 × 10 ^{−5} | 4.85 × 10 ^{−7} |

12 | 9.48 × 10 ^{−6} | 9.48 × 10 ^{−6} | 9.48 × 10 ^{−10} |

13 | 7.5 × 10 ^{−8} | 7.5 × 10 ^{−8} | 7.5 × 10 ^{−9} |

14 | 8 × 10 ^{−6} | 8 × 10 ^{−6} | 8 × 10 ^{−8} |

15 | 4.8 × 10 ^{−8} | 4.8 × 10 ^{−8} | 4.8 × 10 ^{−9} |

16 | 9.1 × 10 ^{−9} | 9.1 × 10 ^{−9} | 9.1 × 10 ^{−9} |

17 | 8.92 × 10 ^{−7} | 8.92 × 10 ^{−7} | 8.92 × 10 ^{−8} |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Taweesin, K.; Seeboonruang, U.; Saraphirom, P.
The Influence of Climate Variability Effects on Groundwater Time Series in the Lower Central Plains of Thailand. *Water* **2018**, *10*, 290.
https://doi.org/10.3390/w10030290

**AMA Style**

Taweesin K, Seeboonruang U, Saraphirom P.
The Influence of Climate Variability Effects on Groundwater Time Series in the Lower Central Plains of Thailand. *Water*. 2018; 10(3):290.
https://doi.org/10.3390/w10030290

**Chicago/Turabian Style**

Taweesin, Korrakoch, Uma Seeboonruang, and Phayom Saraphirom.
2018. "The Influence of Climate Variability Effects on Groundwater Time Series in the Lower Central Plains of Thailand" *Water* 10, no. 3: 290.
https://doi.org/10.3390/w10030290